Q51 / 160 · AP EAMCET 2024 (20 May Shift 1) · Mathematics

If $2 x^2+3 x-2=0$ and $3 x^2+a x-2=0$ have one common root then the sum of all possible values of $a$ is

  • A
    $-3.5$
  • Correct answer
    B
    $7.5$
  • C
    $-7.5$
  • D
    $-1.5$

Solution

$2 x^2+3 x-2=0 \quad \Rightarrow x=-2, \frac{1}{2}$ If $x=-2$ is the common root with $3 x^2+a x-2=0$ then $3(-2)^2+a(-2)-2=0 \Rightarrow a=5$ If $x=\frac{1}{2}$ is the common root with $3 x^2+a x-2=0$ then $3\left(\frac{1}{2}\right)^2+\frac{a}{2}-2=0 \Rightarrow a=2.5$ So, sum of all possible values of $a=7.5$

Hence, the correct answer is option: 'B'.

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